Abstract:
We consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid. The plate is modelled by Reissner-Mindlin equations while the fluid is described in terms of displacement variables. This formulation leads to a symmetric eigenvalue problem. Reissner-Mindlin equations are discretized by a mixed method, the equations for the fluid with Raviart-Thomas elements and a non conforming coupling is used on the interface. In order to prove that the method is locking free we consider a family of problems, one for each thickness t > 0, and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t → 0. We prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t. © Springer-Verlag 2000.
Registro:
| Documento: |
Artículo
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| Título: | Finite element analysis of the vibration problem of a plate coupled with a fluid |
| Autor: | Durán, R.G.; Hervella-Nieto, L.; Liberman, E.; Rodríguez, R.; Solomin, J. |
| Filiación: | Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina
Departamento de Matemática, Facultade de Informática, Universidade da Coruña, 15071 - A Coruña, Spain
Comn. Invest. Cie. Provincia B., Departamento de Matemática, Universidad Nacional de La Plata, C.C. 172, 1900 - La Plata, Argentina
Depto. de Ing. Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 172, 1900 - La Plata, Argentina
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| Año: | 2000
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| Volumen: | 86
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| Número: | 4
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| Página de inicio: | 591
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| Página de fin: | 616
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| DOI: |
http://dx.doi.org/10.1007/PL00005411 |
| Título revista: | Numerische Mathematik
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| Título revista abreviado: | Numer. Math.
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| ISSN: | 0029599X
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0029599X_v86_n4_p591_Duran |
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Citas:
---------- APA ----------
Durán, R.G., Hervella-Nieto, L., Liberman, E., Rodríguez, R. & Solomin, J.
(2000)
. Finite element analysis of the vibration problem of a plate coupled with a fluid. Numerische Mathematik, 86(4), 591-616.
http://dx.doi.org/10.1007/PL00005411---------- CHICAGO ----------
Durán, R.G., Hervella-Nieto, L., Liberman, E., Rodríguez, R., Solomin, J.
"Finite element analysis of the vibration problem of a plate coupled with a fluid"
. Numerische Mathematik 86, no. 4
(2000) : 591-616.
http://dx.doi.org/10.1007/PL00005411---------- MLA ----------
Durán, R.G., Hervella-Nieto, L., Liberman, E., Rodríguez, R., Solomin, J.
"Finite element analysis of the vibration problem of a plate coupled with a fluid"
. Numerische Mathematik, vol. 86, no. 4, 2000, pp. 591-616.
http://dx.doi.org/10.1007/PL00005411---------- VANCOUVER ----------
Durán, R.G., Hervella-Nieto, L., Liberman, E., Rodríguez, R., Solomin, J. Finite element analysis of the vibration problem of a plate coupled with a fluid. Numer. Math. 2000;86(4):591-616.
http://dx.doi.org/10.1007/PL00005411
